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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Generalized Convexity, Generalized Monotonicity: Recent Results: Recent Results

Generalized Convexity, Generalized Monotonicity: Recent Results: Recent Results

Crouzeix, Jean-Pierre
Martinez Legaz, Juan Enrique
Volle, Michel

Hardcover

Series: Nonconvex Optimization and Its Applications, Book 27

EconomicsCalculusGeneral Mathematics

ISBN10: 079235088X
ISBN13: 9780792350880
Publisher: Springer Nature
Published: Aug 31 1998
Pages: 471
Weight: 1.90
Height: 1.06 Width: 6.14 Depth: 9.21
Language: English
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo- metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man- agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob- lems.

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